The parent function f(x) = log3x has been transformed by reflecting it over the x-axis, stretching it vertically by a factor of two and shifting it down three units. which function is representative of this transformation?

g(x) = log3(-2x) - 3
g(x) = log3(2x) + 3
g(x) = -2log3(x) - 3
g(x) = 2log3(x) + 3

Third option.

Step-by-step explanation:

Some transformations for a function f(x), are:

If , the function is shifted down "k" units.

If , the function is shifted up "k" units.

If , and , the functio is stretch vertically by a factor of "b".

If  , the function is reflected over the x-axis.

Therefore, knowing that the parent function  was transformated by reflecting it over the x-axis, stretching vertically by a factor of 2 and shifting it down 3 units, we can determine that the following function represents the transformation:

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt